Puri - Konark

I will be visiting Orissa from Bangalore. I have two days at orissa. I will be arriving at Bhubaneshwar at 2:30 a.m. (Morning). Will proceed to Puri same day. My iternary will be :
Day 1: Reach Bhubaneshwar at 2:30 a.m. Proceed to Puri by bus / train.
Reach Puri at 5:30 .a.m. Hotel.
Visit Puri Jagannath temple in the first half.
Lunch. Proceed to Konark Sun temple by taxi / Shared autos.
Back to Puri @ 8:00p.m.
Day 2: Visit Puri Beach, Jagannath temple.
Proceed to Bhubaneshwar. Visit dhauli Enroute.
Visit RajaRani temple and Lingaraj Temple.
Train at 6:00 p.m. (to Howrah)

My questions are:
1. Will I get bus to Puri (from Bhubaneshwar) at eraly morning ? Will it be overcrowded ?
2. How will be the crowd at Puri Jagannath temple on sunday ? Is there any paid special entrance to the temple ?
3. Is it safe to return back to puri (from Konark) at 8:00 p.m.?
4. Temple timings of rajarani and Lingaraj temple ?

1. Yes, bus service starts at 5:30AM.
2. Should be crowded on Sunday, approach to any Panda for special treatment. Hmm, they behave like beggars, its very shameful, sometime Panda forces for money. Temple management is very corrupt, its very shameful. Even they don't install new ceiling fans, forget the AC and carpet cleaning, leave it... don't like to say more...

My quick views,
1-Better to catch a train to Puri from Bhubaneswar Station.http://erail.in/ would help.Other wise go to Mueseum square to catch a Bus to puri.Early morning Bus would be relativley vacant.I would suggest the train option.
2-The temple would be little crowded as normal.Very unfortunate to say that the Pandas(priests) in Puri temple are the most uncivilized,arrogant and rowdys to say the least.Try to avoid them politily and go for a Darshan on your own.Dont ask for any special darshan and like ,if you do so ready to fork out a significant sum.These Pandas are more of a extornists inside the temple.Being from Odisha this makes me feel very Sad,but cant help.
3-If you travel by your own cab it is relatively safe at 8 pm.But advice you to make it little early.
4-Rajarani temple is open till 6 pm and lingaraj temple also.

A rickshaw costs around 400 from bhubaneswar to Puri, maybe you could find someone to share the ride if you miss the bus.

Jagannath temple and the Sun temple are great to visit, i suggest you could pass Rajarani and Lingaraj temple and head to Chilika lake instead. You will get a bus to one of Chilika's entrances(the one which has the dolphin sighting) from Puri. But one whole day will go in that and the best time to actually sight the dolphins is early morning.

Also, look up 'surfing yogis', they manage a surf and stand up paddle spot at Puri-Konark marine drive. Great people. If you catch a bus from Konark, it's situated around 30 minutes before Puri.
I had a great time in Odisha earlier this year, but I found the rickshawwalas really cunning. So be aware of that.

I had been to Orissa and trip was good
Day 1: I reached Bhubaneshwar at 3:00 a.m. and got a bus to Puri at 4:00 a.m. Reached Puri at 6:15 a.m. Checked in to Hotel. Refreshed. Proceeded to Konark Via Ramchandi by bus. Visited Ram chandi and later to Konark. Back to Konark by 2:30 p.m. Had lunch. Rest at hotel. Went to Puri beach at 5:00 and enjoyed with my daughter till 6:15 p.m. Later went to Temple. The rush was less. We were able to have good darshan of the lord Jagannath. Back to Hotel by 8:30 p.m.
Day 2: Had morning darshan of Lord jagannath. Proceeded to Bhubaneshwar by bus. Reached Bhubaneshwar at 10:30 a.m. Took a auto for Rs.400 for visiting Dhauli, Lingaraj temple, Raja Rani temple, Mukteshwar temple, Ram Mandir, Bindu Sarovar and back to Bhubaneshwar at 4:00p.m. Train was at 6:00 p.m.
Everything went smoothly as planned..... :-)

I find it interesting that you "proceeded to Konark via Ramchandi ..." and "Visited Ramchandi ...". If so, it seems like you were at Ramchandi for only a few hours. Is that correct?
If so, can you please let me know whether you would recommend that I do the same? I have the time to do so but I do not know whether it is worthwhile. What are the highlights/activities there? How much does it cost? Please note that I am not interested in an overnight stay at that place.

Ramchandi is a place 5km before konark on Puri-Konark road. The buses between puri and konark has a stop at Ramchandi. There is a temple at Ramchandi. I was there only for 30 minutes. I felt it was worth visitng. You have to walk few meters from the main road. After Ramchandi, you can proceed to chandrabhaga beach and then to Konark.
Route: (Puri- konark highway)
Puri--> Ramchandi --> Chandrabhaga --> Konark.